Answer:
Solution given:
radius [r]=2cm
height [h]=8cm
total surface area of cylinder=?
we have
total surface area of cylinder=2πr²+2πrh
- 2πr(r+h)
- 2π*2(2+8)
- 40π or 125.66cm²
<u>total surface area of cylinder</u><u>40π or 125.66cm²</u><u>.</u>
The vertex is (-4,-3)
The axis of symmetry is x=-4
and the transformations are:
Answer
h^-1(x)= x+43
Explanation
h(x)=x-43
Use substitution
y=x-43
Interchange the variables
x=y-43
Swap the sides
y-43=x
Move the constant to the right
y=x+43
Use substitution
h^-1(x)=x+43
<u>Given</u>:
Given that the graph OACE.
The coordinates of the vertices OACE are O(0,0), A(2m, 2n), C(2p, 2r) and E(2t, 0)
We need to determine the midpoint of EC.
<u>Midpoint of EC:</u>
The midpoint of EC can be determined using the formula,

Substituting the coordinates E(2t,0) and C(2p, 2r), we get;

Simplifying, we get;

Dividing, we get;

Thus, the midpoint of EC is (t + p, r)
Hence, Option A is the correct answer.
General Idea:
The volume of cylinder is given by
, where r is the radius and h is the height of the cylinder.
Applying the concept:
Step 1: We need to find the volume of full cylinder with the given dimensions using the formula.
Volume of full cylinder 
Volume of half cylinder 
Step 2: Let x be the number of minutes of filling the sand.
of sand filled every 15 seconds, there are four 15 seconds in a minute.
So volume of sand filled in 1 minute
.
of sand taken out of cylindrical vase every minute.
Net volume of sand filled in 1 minute = Volume of sand filled in the vase in one minute - Volume of sand taken out in 1 minute
Net volume of sand filled in 1 minute
Volume of sand filled in x minutes
.
We need to set up an equation to find the number of minutes need to fill half the volume in cylindrical vase.

Conclusion:
The number of minutes required for the base be half filled with sand is 57